To find the equation of the line of best fit and the correlation coefficient for this data, we can use a graphing calculator or statistical software.
Using a graphing calculator, we can input the data into lists and then use the linear regression function to find the line of best fit and the correlation coefficient. Here are the steps:
Press the STAT button and select Edit.
Enter the years into L1 and the number of students into L2.
Press the STAT button again and select CALC.
Choose LinReg(ax+b) and press ENTER.
For Xlist, select L1, and for Ylist, select L2.
Make sure the frequency list is set to 1.
Press ENTER to see the results.
The calculator should display the equation of the line of best fit in the form y = mx + b, where m is the slope and b is the y-intercept. It should also display the correlation coefficient r, which measures the strength and direction of the linear relationship between the two variables.
According to the given data, the equation of the line of best fit is y = 14x + 478.7, rounded to the nearest tenth. This means that for every one-year increase in the x variable (year), we expect to see a 14-unit increase in the y variable (number of X students), on average. The y-intercept of the line is 478.7, rounded to the nearest tenth, which represents the predicted value of y when x equals zero (i.e., the year 0, which does not exist in this context).
The correlation coefficient is given as 1, rounded to the nearest tenth. This indicates a perfect positive correlation between the year and the number of X students, meaning that as the year increases, so does the number of X students, and the relationship is very strong. This suggests that there may be some underlying factor or trend that is driving this increase over time, such as population growth or changes in educational policies.